基于主成分分析的薄壁结构截面特征形变识别研究

Recognition of characteristic deformation of thin-walled structure sections based on principal component analysis

针对薄壁结构一维高阶模型求解复杂、效率低等问题,提出了一种基于主成分分析的薄壁结构截面特征识别方法。首先,构建了一组基函数捕捉截面变形,建立了薄壁结构的一维高阶模型,基函数被集成在动力学方程中,并通过求解相关的广义特征值问题实现了解耦;然后,基于主成分分析分解特征向量,识别出基函数的轴向变化模式,每个特征向量被正交分解成对应变化模式的分量,并构建了权重矩阵线性组合基函数;最后,以识别出的变形模式简化了初始动力学方程。研究结果表明:识别出的变形模式具有再现薄壁结构三维振型的能力,与ANSYS模型相比较,高阶模型的前10阶固有频率误差在1.94%以内;该结果为提高薄壁结构动力学模型的计算效率提供了理论依据。

Aiming at the problems of complex and low-efficiency one-dimensional high-order model of thin-walled structures,a method of identifying cross-sectional deformation of thin-walled structures based on principal component analysis was proposed.First,a set of basis functions was constructed to capture the section deformation and one-dimensional high-order model of the thin-walled structure was established.The basis functions were integrated into the dynamic equations and decoupled by solving the related generalized eigenvalue problems.Then,the feature vector was decomposed based on principal component analysis to identify the axial change pattern of the basis function.Each feature vector was orthogonally decomposed into components corresponding to changing patterns,and weight matrix linear combinatorial basis functions were constructed.Finally,the initial dynamics equation was simplified with the identified deformation patterns.The results show that the identified deformation mode has the ability to reproduce the three-dimensional mode shape of thin-walled structures.Comparing with the ANSYS model,the first ten-order natural frequency error of the high-order model is within 1.94%,which provides a theoretical basis for improving the calculation efficiency of the dynamic model of thin-walled structures.